- Skeel R. Thirteen ways to estimate global error // Numerische Mathematik. 1986. V. 48. P. 1-20.
- Roy C.J., Oberkampf W.L. A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing // Computer Methods in Applied Mechanics and Engineering. 2011. V. 200. № 25-28. P. 2131-2144.
- Repin S. A posteriori estimates for partial differential equations. Walter de Gruyter., 2008. V. 4.
- Repin S. A unified approach to a posteriori error estimation based on duality error majorants // Mathematics and Computers in Simulation. 1999. V. 50. № 1-4. P. 305-321. EDN: LFERLL
- Repin S., Frolov M. A posteriori error estimates for approximate solutions of elliptic boundary value problems // Computational Mathematics and Mathematical Physics. 2002. V. 42. № 12. P. 1704-1716. EDN: SSAEIV
- Synge J.L. The Hypercircle in Mathematical Physics. London: CUP., 1957.
- Oden J., Prudhomme S. Goal-oriented error estimation and adaptivity for the finite element method // Computers and Mathematics with Appl. 2001. V. 41. P. 735-756. EDN: AMGSCV
- Prudhomme S., Oden J. On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors // Computer Methods in Applied Mechanics and Engineering. 1999. V. 176. P. 313-331. EDN: ADHKNB
- Ainsworth M., Oden J. A posteriori error estimation in finite element analysis. N.Y.: Wiley-Interscience, 2000.
-
Carpenter M., Casper J. Accuracy of shock capturing in two spatial dimensions // AIAA Journal. 1999. V. 37. № 9. P. 1072-1079. DOI: 10.2514/2.835
-
Babuska I., Osborn J. Can a finite element method perform arbitrarily badly? // Mathematics of Computation of the American Mathematical Society. 2000. V. 69. № 230. P. 443-462.
-
Godunov S.K., Manuzina Yu.D., Nazareva M.A. Experimental analysis of convergence of the numerical solution to a generalized solution in fluid dynamics // Computational Mathematics and Mathematical Physics. 2011. V. 51. P. 88-95. EDN: OIBXML
-
Linss T., Kopteva N. A Posteriori Error Estimation for a Defect-Correction Method Applied to Convection-Diffusion Problems // Int. J. of Numerical Analysis and Modeling. 2009. V. 1. № 1. P. 1-16. EDN: MYDYRJ
-
Shokin Yu.I. Method of differential approximation. Springer-Verlag, 1983.
-
Banks J., Hittinger J., Woodward C. Numerical error estimation for nonlinear hyperbolic PDEs via nonlinear error transport // Computer Methods in Applied Mechanics and Engineering. 2012. V. 213. P. 1-15. DOI: 10.1016/j.cma.2011.11.021
-
Rauser F., Marotzke J., Korn P. Ensemble-type numerical uncertainty quantification from single model integrations // Journal Comp. Physics. 2015. V. 292. P. 30-42. DOI: 10.1016/j.jcp.2015.02.043
-
Johnson C. On computability and error control in CFD // International J. for Numerical Methods in Fluids. 1995. V. 20. P. 777-788. DOI: 10.1002/fld.1650200806
-
Babuska I., Rheinboldt W. A posteriori error estimates for the finite element method // International Journal for Numerical Methods in Engineering. 1978. V. 12. P. 1597-1615. DOI: 10.1002/nme.1620121010
-
Roy Ch., Raju A. Estimation of discretization errors using the method of nearby problems // AIAA Journal. 2007. V. 45. № 6. P. 1232-1243. DOI: 10.2514/1.24282
-
Guide for the Verification and Validation of Computational Fluid Dynamics Simulations, American Institute of Aeronautics and Astronautics, AIAA-G-077-1998, Reston, VA, 1998.
-
Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer, ASME V&V 20-2009, 2009.
-
Federal standard P 57700.12-2018. Numerical simulation of supersonic flows for an inviscid gas. Software verification. National standard of the Russian Federation for numerical modeling of physical processes, 2018.
-
Richardson L.F. The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations with an Application to the Stresses in a Masonry Dam // Transactions of the Royal Society of London, Series A. 2010. V. 1908. P. 307-357.
-
Roy Ch.J. Grid Convergence Error Analysis for Mixed -Order Numerical Schemes // AIAA Journal. 2003. V. 41. № 4. P. 595-604.
-
Phillips Tyrone S., Roy Christopher J. Richardson Extrapolation-based Discretization Uncertainty Estimation for Computational Fluid Dynamics // ASME Journal of Fluids Engineering. 2014. V. 136. № 12. 121401.
-
Ortner C. A Posteriori Existence in Numerical Computations // SIAM Journal on Numerical Analysis. 2009. V. 47. № 4. P. 2550-2577.
-
Chernyshenko S.I., Constantin P., Robinson J.C., Titi E.S. A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations // J. of Mathematical Physics. 2007. V. 48. 065204.
-
Bondarev A. Analysis of space-time flow structures by optimization and visualization methods // Transactions on Computational Science XIX, Lecture Notes in Computer Science. 2013. V. 7870. P. 158-168. EDN: RFPWXR
-
Bondarev A., Galaktionov V. Parametric optimizing analysis of unsteady structures and visualization of multidimensional data // International Journal of Modeling, Simulation and Scientific Computing 04 (Supp. 01). 2013.
-
Bondarev A. On the construction of the generalized numerical experiment in fluid dynamics // Mathematica Montisnigri XLII. 2018. P. 52-64.
-
Bondarev A. On visualization problems in a generalized computational experiment // Scientific Visualization. 2019. V. 11. № 2. P. 156-162. DOI: 10.26583/sv.11.2.12 EDN: RNJFRA
-
Bondarev A., Kuvshinnikov A. Analysis of the accuracy of OpenFOAM solvers for the problem of supersonic flow around a cone // Lecture Notes in Computer Science. 2018. V. 10862. P. 221-230. DOI: 10.1007/978-3-319-93713-7_18 EDN: YBSSVV
-
Bondarev A. On the estimation of the accuracy of numerical solutions in CFD problems // LNCS. 2019. V. 11540. P. 325-333. DOI: 10.1007/978-3-030-22750-0_26 EDN: IJMETC
-
Bondarev A., Galaktionov V. Generalized computational experiment and visual analysis of multidimensional data // Scientific Visualization. 2019. V. 11. № 4. P. 102-114. DOI: 10.26583/sv.11.4.09 EDN: DNZGLY
-
Alekseev A., Bondarev A., Galaktionov V., Kuvshinnikov A. On the construction of a generalized computational experiment in verification problems // Matematica Montisnigri XLVIII.
-
OpenFOAM Foundation. http://www.openfoam.org. last accessed 2021/01/08.
-
Alekseev A., Bondarev A. On exact solution enclosure on ensemble of numerical simulations // Mathematica Montisnigri XXXVIII. 2017. P. 63-77.
-
Alekseev A., Bondarev A., Kuvshinnikov A. Verification on the ensemble of independent numerical solutions // LNCS. 2019. V. 11540. P. 315-324. DOI: 10.1007/978-3-030-22750-0_26 EDN: FFETLA
-
Alekseev A., Bondarev A. Estimation of the distance between true and numerical solutions // Computational Mathematics and Mathematical Physics. 2019. V. 59. № 6. P. 857-863. DOI: 10.1134/S0965542519060034 EDN: DWHUCY
-
Alekseev A., Bondarev A., Kuvshinnikov A. On uncertainty quantification via the ensemble of independent numerical solutions // Journal of Computational Science. 2020. V. 42. 101114. DOI: 10.1016/j.jocs.2020.101114 EDN: WUZKJG
-
Alekseev A., Bondarev A., Kuvshinnikov A. Comparative analysis of the accuracy of OpenFOAM solvers for the oblique shock wave problem // Mathematica Montisnigri XLV. 2019. P. 95-105. DOI: 10.20948/mathmontis-2019-45-8
-
Bondarev A., Kuvshinnikov A. Parametric study of the accuracy of OpenFOAM solvers for the oblique shock wave problem // IEEE Proceedings of the 2019 Ivannikov ISPRAS Open Conference 2019. P. 108-112. DOI: 10.1109/ISPRAS47671.2019.00023 EDN: ZQRKUU
-
Bondarev A.E., Galaktionov V.A. Multidimensional data analysis and visualization for time-dependent CFD problems // Programming and Computer Software. 2015. V. 41. № 5. P. 247-252. DOI: 10.1134/S0361768815050023 EDN: UZYVYZ
-
Andreev S.V., Bondarev A.E., Bondarenko A.V., Vizilter Yu.V., Galaktionov V.A., Gudkov A.V., Zheltov S.Yu., Zhukov V.T., Ilovaiskaya E.B., Knyaz V.A., Manukovskii K.V., Novikova N.D., Ososkov M.V., Silaev N.Zh., Feodoritova O.B. A Computational Technology for Constructing the Optimal Shape of a Power Plant Blade Assembly Taking into Account Structural Constraints // Programming and Computer Software. 2017. V. 43. № 6. P. 345-352. DOI: 10.1134/S0361768817060020 EDN: XXEGKL
-
Bondarev A.E., Galaktionov V.A., Kuvshinnikov A.E. Parallel Solutions of Parametric Problems in Gas Dynamics Using DVM/DVMH Technology // Programming and Computer Software. 2020. V. 46. № 3. P. 176-182. DOI: 10.1134/S0361768820030032 EDN: YQSXWP
-
Kurganov A., Tadmor E. New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations // Journal of Computational Physics. 2000. V. 1. P. 241-282. DOI: 10.1006/jcph.2000.6459 EDN: LTVUAN
-
Greenshields C., Wellerr H., Gasparini L., Reese J. Implementation of semi-discrete, non-staggered central schemes in a colocated, polyhedral, finite volume framework, for high-speed viscous flows // International Journal for Numerical Methods in Fluids. 2010. V. 63. № 1. P. 1-21. DOI: 10.1002/fld.2069 EDN: OCGUCP
-
Issa R. Solution of the implicit discretized fluid flow equations by operator splitting // Journal of Computational Physics. 1986. V. 66. № 1. P. 40-65. DOI: 10.1016/0021-9991(86)900999
-
Kraposhin M., Bovtrikova A., Strijhak S. Adaptation of Kurganov-Tadmor numerical scheme for applying in combination with the PISO method in numerical simulation of flows in a wide range of Mach numbers // Procedia Computer Science. 2015. V. 66. P. 43-52. DOI: 10.1016/j.procs.2015.11.007 EDN: WSRTZD
-
Kraposhin M., Smirnova E., Elizarova T., Istomina M. Development of a new OpenFOAM solver using regularized gas dynamic equations // Computers & Fluids. 2018. V. 166. P. 163-175. DOI: 10.1016/j.compfluid.2018.02.010 EDN: XYAUKL
-
Бабенко К.И., Воскресенский Г.П., Любимов A.Н., Русанов В.В. Пространственное обтекание гладких тел идеальным газом. М.: Наука, 1964, 505 с.